There are two main criteria:

Thanks for your reply Jürgen Weippert . Let me understand your answer in a better way, so (a) by 'cross-section' you mean cross-section of the sample used? (b) by 'coupling' you mean to say the overlapping of multiple peaks?

I am sharing XPS spectra of my sample here. As we can see, it has 2 peaks each for Si, Al and P (apart from other element peaks), i.e., both 2s and 2p peaks. So, which peak out of these two for Si, P and Al should be considered for our final analysis, in terms of peak shift and/or deconvolution, and why?

Also, I am referring to the website https://www.thermofisher.com/in/en/home/materials-science/learning-center/periodic-table.html for analysis.

Here, if we choose Si element for an example, we see that the primary region for Si is given as Si2p. Likewise, for each element, the primary regions are given in this website. I have seen in the articles published that authors are showing the primary region spectra only for an element and analyzing on the basis of it, instead of the other orbital peaks. My question is how is it defined which would be the primary region and how is it chosen for each element, as I can see that the primary regions are shown in the published articles.

a) No, cross section has nothing to do with sample dimensions, it is the cross section for the ionization process as you can find them in the Yeh/Lindau or Scofield tables. These are the main factors in XPS sensitivities of a certain peak. On this subject please also see this manual, starting on page 67:

http://uhv.cheme.cmu.edu/manuals/M470101.pdf

b) Overlapping of different peaks is what we want to avoid here. Depending on the coupling interaction between the electrons peaks may be split up in e.g. a p1/2 and a p3/2 part and if these are still close together, this may make your deconvolution pretty hard.

But generally, the Thermo Fisher guide is a pretty good source for element-specific information.